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A-LevelMathematicsLogarithmic and exponential functions9709/22 · Oct/Nov 2024 · Q13 Marks

Use logarithms to show that the equation 5⁸ʸ = 6⁷ˣ can be expressed in the form y = kx. Give the value of the constant k correct to 3 significant figures.

  1. Use logarithms to show that the equation 5⁸ʸ = 6⁷ˣ can be expressed in the form y = kx. Give the value of the constant k correct to 3 significant figures.[3]

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

  1. [M1] Apply logarithms correctly and apply power law at least once
  2. [DM1] Obtain y = 7ln6 / 8ln5 x or equivalent perhaps involving decimals
  3. [A1] Obtain k = 0.974 or state y = 0.974x

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About this question

Topic
Logarithmic and exponential functions, A-Level Mathematics (syllabus 9709). Structured question, 3 marks.
Source
A-Level Mathematics, Oct/Nov 2024 Paper 2 Variant 2, question 1.

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